International Association
for Cryptologic Research

Symbolic computations with usage of algebraic graphs A(n; F_q) and A(n;,F_q[x_1, x_2,..., x_n]) were used for the development of various cryptographic algorithms because the length of their minimal cycle (the girth) tends to infinity when n is growing. It was announced recently that for each commutative integrity ring the girth of A(n, K) is ≥ 2n. In this paper we present essentially shorter closed proof of this statement and evaluate the girth of some induced subgraphs of A(n; K[x_1, x_2, ..., x_n]).